Question

If d is the HCF of 55 and 65 find x, y satisfying d = 55x + 65y also show that x and y are not unique

Answer 1

Answer:

Step-by-step explanation:

65= 55*1 + 10 [equation 1]

55= 10*5 + 5 [equation 2]

10= 5*2 + 0 [equation 3]

HCF is the divisor at the last stage ie:5

d=5

so ATQ,

d= 55x +65y [equation 4]

5=55x + 65y

now

from equation 2,

5= 55 - 10*5 [equation 5]

from equation 1,

10= 65 - 55*1

substituting value of 10 in equation 5

5= 55 - (65-55*1)*5

5= 55 - 65*5 + 55*5

5= 55*6 +65*(-5) [equation 6]

comparing equation 4 and and equation 6

x=6 and y= -5